I have no experience between US/UK, but in general I am quite happy with sending packages through shipping. Where with airlines weight is key, in shipping it is volume. Most shipping is done through containers. This is both a +1 and a -1.
Positive is that you don't have to bother about a kg more or less, as long as it fits the volume you are more or less okay. The problem is that a container is also the unit. If you can fill a container, shipping is an interesting way of transporting.
If you have less volume to sent then a container it gets complicated. If you live close to a large immigration/expat population from the country to which you want to sent a package you might find various companies that are able to fill a container by combining various packages.
This is what I have been doing. Prices can be as low as € 45,- 240L 48 x 48 x 93 cm for a shipment between Europe and South America.
As said I have no experience with shipping between the UK and the US. The search key that might help locating a similar service is "parcel services". However, I did a google search on UK USA parcel services and all results pointed to usual (expensive) parties (DHL, Fedex, etc).
If you are living close to a international port, you might want to drive around in the business area and you will see quite some companies offering parcel services. Most will not offer services to individuals, but they certainly will be able to point you in the right direction.